5332
J. Chem. Eng. Data 2010, 55, 5332–5339
PGT Measurements of the (Ethanol + Linalool), (Propan-1-ol + Linalool), and (Propan-2-ol + Linalool) Mixtures: Cubic and Statistical Associating Fluid Theory-Based Equation of State Analyses Marcos Torcal,† M. Isabel Teruel,† Josefa Garcı´a,‡ Jose´ S. Urieta,† and Ana M. Mainar*,† Group of Applied Thermodynamics and Surfaces (GATHERS), Aragon Institute for Engineering Research (I3A), Facultad de Ciencias, Universidad de Zaragoza, Zaragoza 50009, Spain, and Departamento de Fı´sica Aplicada, Edificio de Ciencias Experimentales, Universidad de Vigo, 36310 Vigo, Spain
The density of the asymmetrical binary systems (ethanol + linalool), (propan-1-ol + linalool), and (propan2-ol + linalool) has been measured (660 points) for nine different compositions including the pure compounds at four temperatures in the range (283.15 to 328.15) K and 5 isobars up to 20 MPa with a vibrating-tube densimeter. The experimental expanded uncertainty is estimated to be ( 0.5 kg · m-3. The isothermal compressibility, the isobaric thermal expansion, and the excess molar volume were derived from the experimental density data, revealing that a volume contraction occurs for these binary mixtures. Three different equations of state (EOS’s), Peng-Robinson (PR), statistical associating fluid theory (SAFT), and perturbedchain statistical associating fluid theory (PC-SAFT), were applied to predict the volumetric behavior of the alkanolic mixtures. The best predictions were achieved with the PC-SAFT equation of state.
Introduction Experimental knowledge of thermophysical properties of organic liquids and their mixtures is of great interest for both industrial and theoretical purposes. Information about pressure and temperature dependencies of such properties allows thermodynamic modeling based on equations of state (EOS’s) and statistical mechanics to be checked. The rationalization of highpressure methods permits the development of green, environmentally friendly processes such as supercritical extraction processes (SCE), which are being applied successfully. The present work involves the experimental and theoretical study of three binary mixtures made up of (()-3,7-dimethyl1,6-octadien-3-ol, also known as (()-linalool, and ethanol, propan-1-ol, or propan-2-ol. All of the solvents here used are considered as friendly compounds in a green chemistry context, and they are destined to improve the cosolvent-assisted SCE of valuable substances contained in vegetable matrix.1 Linalool is the main component in extracts of a great number of vegetable species such as coriander, basil, and orange blossom among others. Its minimal toxicity for humans and its use as a chemical intermediate (e.g., vitamin E) make linalool one of the substances most common in cosmetic, food, and pharmacology industries. The pressure and temperature ranges of measurement, (0.1 to 20) MPa and (283.15 to 328.15) K, were selected due to the experimental conditions employed in our laboratory2 when extracting volatile oils containing linalool using supercritical CO2 and alcohols as entrainers. The study also includes isobaric thermal expansivities and isothermal compressibilities, as well as the excess volumes. Besides the experimental data, the modeling of the thermophysical properties is the nexus between the fundamental * Corresponding author. E-mail:
[email protected]. Fax: +34 976 761 202. Phone: +34 976 761 195. † Universidad de Zaragoza. ‡ Universidad de Vigo.
Figure 1. Molecule of R-(-)-linalool enantiomer.
knowledge and its later application to develop industrial processes. To this extent, three EOS’s, as predictive, were tested: Peng-Robinson (PR),3 the statistical associating fluid theory (SAFT),4-6 and the perturbed-chain statistical associating fluid theory (PC-SAFT).7,8
Experimental Section Chemicals and Preparation of Samples. (()-Linalool (purity, mole fraction > 0.982) and ethanol (purity, mole fraction > 0.999) were supplied from Aldrich. Propan-1-ol (purity, mole fraction > 0.999) and propan-2-ol (purity, mole fraction > 0.999) were from Scharlab (Barcelona, Spain). The stated purities of the chemicals were checked by gas chromatography analysis. All liquids were used without further purification. Figure 1 shows the more stable conformation of the R-(-)-enantiomer of linalool obtained by a method of molecular mechanics force field (MM2). Mixtures were set by weighing on a Mettler Toledo AB265-S balance, whose precision is ( 10-5 kg. They were prepared in 11 mL airtight glass vials. The expanded uncertainty (coverage factor, k ) 2) in the mole fraction was ( 0.0001. Experimental DeWice. The experimental device used is similar to others previously used by Sousa et al.9 and Esteve et al.10 A detailed description of the apparatus, together with the setup
10.1021/je100581m 2010 American Chemical Society Published on Web 10/05/2010
Journal of Chemical & Engineering Data, Vol. 55, No. 11, 2010 5333 Table 1. Density, G, as a Function of Temperature, Pressure, and Mole Fraction for Mixtures (Ethanol + Linalool), (Propan-1-ol + Linalool), and (Propan-2-ol + Linalool) F/kg · m-3 p/MPa x1
0.1
5
10
p/MPa 15
20
0.1
5
10
15
20
Ethanol (1) + Linalool (2) 0 0.1129 0.1935 0.3049 0.4023 0.5121 0.6055 0.7008 0.8009 0.9009 1
869.2 866.8 865.6 862.7 859.9 855.3 850.3 843.1 832.7 818.2 797.7
872.3 869.9 868.7 866.0 863.1 858.5 853.5 846.5 836.3 822.0 801.8
T/K ) 283.15 875.2 872.9 871.7 869.0 866.1 861.6 856.8 849.7 839.6 825.5 805.6
878.2 875.9 874.8 872.1 869.2 864.8 860.1 853.0 843.1 829.2 809.6
881.0 878.8 877.6 874.9 872.1 867.7 862.9 856.1 846.3 832.5 813.1
856.9 854.5 853.4 850.5 847.6 843.0 838.0 830.9 820.6 805.9 784.9
860.1 857.8 856.7 853.9 851.0 846.5 841.4 834.6 824.4 809.9 789.3
T/K ) 298.15 863.5 861.1 860.0 857.2 854.4 850.0 845.1 838.2 828.1 813.9 793.6
866.6 864.3 863.2 860.5 857.7 853.2 848.4 841.6 831.7 817.7 797.7
869.6 867.4 866.3 863.6 860.8 856.4 851.7 844.9 835.1 821.3 801.6
0 0.1129 0.1935 0.3049 0.4023 0.5121 0.6055 0.7008 0.8009 0.9009 1
844.1 841.7 840.6 837.8 834.7 830.2 825.3 818.0 807.9 793.2 771.9
847.8 845.4 844.4 841.6 838.6 834.1 829.3 822.3 812.1 797.7 776.8
T/K ) 313.15 851.3 849.0 847.9 845.2 842.3 837.8 833.1 826.1 816.1 801.9 781.3
854.8 852.5 851.4 848.7 845.8 841.4 836.7 829.8 820.0 806.0 785.7
858.1 855.8 854.8 852.1 849.2 844.9 840.2 833.4 823.7 809.8 789.9
831.3 828.9 827.8 824.9 821.8 817.3 812.3 805.2 794.9 780.2 758.6
835.2 832.9 831.8 828.9 825.9 821.4 816.6 809.5 799.4 784.9 763.8
T/K ) 328.15 839.1 836.9 835.8 832.9 829.9 825.5 820.6 813.9 803.9 789.6 768.9
842.7 840.5 839.4 836.6 833.7 829.3 824.5 817.8 808.0 793.9 773.6
846.3 844.1 843.0 840.3 837.3 833.0 828.4 821.6 811.9 798.1 778.1
878.7 876.2 874.1 871.4 868.3 864.8 859.9 853.3 845.8 835.5 821.7
881.5 879.0 876.9 874.4 871.3 867.7 862.8 856.3 848.8 838.6 824.9
857.3 854.8 852.7 849.9 846.8 843.2 838.2 831.6 824.0 813.4 799.0
860.6 858.1 856.0 853.3 850.2 846.7 841.7 835.1 827.7 817.2 803.0
T/K ) 298.15 863.9 861.4 859.4 856.6 853.6 850.1 845.2 838.7 831.2 820.8 806.9
867.0 864.6 862.6 859.9 856.8 853.3 848.5 842.0 834.6 824.4 810.6
870.0 867.7 865.6 863.0 859.9 856.5 851.6 845.2 837.9 827.8 814.1
855.0 852.8 850.8 848.1 845.1 841.5 836.7 830.4 823.2 813.1 799.3
858.4 856.1 854.1 851.5 848.4 844.9 840.2 833.9 826.7 816.7 803.1
831.7 829.4 827.3 824.5 821.3 817.7 812.8 806.3 799.0 788.7 774.5
835.6 833.3 831.2 828.5 825.3 821.8 816.9 810.5 803.3 793.1 779.1
T/K ) 328.15 839.5 837.2 835.2 832.5 829.3 825.8 821.0 814.7 807.5 797.5 783.7
843.1 840.9 838.8 836.2 833.0 829.5 824.8 818.5 811.4 801.5 787.8
846.7 844.4 842.4 839.8 836.7 833.2 828.5 822.3 815.2 805.3 791.9
Propan-1-ol (1) + Linalool (2) 0 0.1070 0.2060 0.3066 0.4064 0.5010 0.6034 0.7055 0.7985 0.8980 1
869.5 867.0 864.9 862.1 859.0 855.4 850.3 843.7 835.9 825.2 810.9
872.6 870.2 868.1 865.4 862.2 858.6 853.6 847.0 839.3 828.8 814.7
T/K ) 283.15 875.7 873.1 871.0 868.3 865.2 861.6 856.7 850.0 842.4 832.0 818.1
0 0.1070 0.2060 0.3066 0.4064 0.5010 0.6034 0.7055 0.7985 0.8980 1
844.5 842.1 840.1 837.3 834.1 830.5 825.6 819.1 811.6 801.2 786.8
848.2 845.8 843.8 841.1 837.9 834.4 829.5 823.1 815.6 805.3 791.2
T/K ) 313.15 851.6 849.3 847.3 844.6 841.5 838.0 833.2 826.8 819.4 809.2 795.3
878.7 875.5 872.1 868.1 863.7 858.6 852.2 844.9 835.1 820.4 805.2
881.5 878.5 875.0 870.9 866.7 861.6 855.3 848.0 838.4 823.7 808.9
857.3 854.1 850.5 846.3 841.7 836.4 829.7 821.9 812.0 796.8 781.2
860.6 857.4 853.9 849.8 845.2 839.9 833.3 825.6 815.9 800.9 785.5
T/K ) 298.15 863.9 860.8 857.3 853.2 848.7 843.5 837.0 829.4 819.7 804.9 789.7
867.0 864.0 860.5 856.5 852.0 846.9 840.4 832.9 823.4 808.8 793.8
870.0 867.0 863.6 859.6 855.2 850.1 843.7 836.4 826.9 812.4 797.6
855.0 852.1 848.6 844.5 840.0 834.8 828.2 820.6 811.1 796.7 781.9
858.4 855.4 852.0 847.9 843.5 838.3 831.8 824.4 814.9 800.7 786.1
831.7 828.5 824.8 820.4 815.5 809.9 802.8 794.9 784.8 769.8 754.4
835.6 832.5 828.8 824.5 819.7 814.2 807.2 799.4 789.5 774.8 759.6
T/K ) 328.15 839.5 836.4 832.8 828.6 823.9 818.4 811.6 803.9 794.2 779.7 764.8
843.1 840.1 836.5 832.3 827.8 822.3 815.6 808.0 798.4 784.1 769.5
846.7 843.6 840.2 836.0 831.5 826.1 819.5 812.0 802.6 788.4 774.0
Propan-2-ol (1) + Linalool (2) 0 0.1031 0.2049 0.3054 0.4056 0.5022 0.6050 0.7008 0.7981 0.9092 1
869.5 866.3 862.7 858.7 854.1 848.8 842.3 834.6 824.5 809.3 793.7
872.6 869.5 865.9 861.9 857.4 852.2 845.7 838.1 828.2 813.1 797.5
T/K ) 283.15 875.7 872.5 869.0 864.9 860.5 855.3 848.9 841.4 831.6 816.6 801.3
0 0.1031 0.2049 0.3054 0.4056 0.5022 0.6050 0.7008 0.7981 0.9092 1
844.5 841.4 837.7 833.4 828.7 823.2 816.4 808.5 798.6 783.6 768.1
848.2 845.1 841.5 837.3 832.6 827.2 820.6 812.8 803.0 788.2 773.0
T/K ) 313.15 851.6 848.6 845.1 840.9 836.3 831.0 824.4 816.8 807.1 792.5 777.5
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Journal of Chemical & Engineering Data, Vol. 55, No. 11, 2010
and validation of the equipment, was also done in the literature.11 The measuring principle lays on the determination of the oscillation period of an U-shaped tube that contains the sample. The uncertainty in the control of temperature is ( 0.01 K. The pressure of the system was controlled by two pressure transmitters (STW-A09), with ( 0.1 % full scale uncertainty of measurement, one operating up to 16 MPa and the other up to 70 MPa. The overall experimental expanded uncertainty (k ) 2) in the reported density values was estimated to be ( 0.5 kg · m-3.
Results Densities. The experimental densities, F, for pure liquids and binary mixtures alkanol + linalool were measured at four temperatures (283.15, 298.15, 313.15, and 328.15) K and several pressures from (0.1 to 20) MPa in steps of 5 MPa. The experimental results appear in Table 1. Figure 2a shows the relative deviation between experimental and bibliographic data for ethanol (< 0.1 %).12-20 Figure 2b,c includes the relative deviations for propan-1-ol and propan-2-ol between our experimental results and interpolated values from the literature.21-24 The absolute differences are lower than 0.2 %. For each composition, the compressed liquid densities were correlated with the modified Tait relationship:25
F(P,T)/kg · m3 ) F(0.1 MPa,T)/kg · m3 × B(T)/MPa + P/MPa 1 - C(T) ln B(T)/MPa + 0.1 MPa
(
)
-1
(1)
where C(T) and B(T) are temperature-dependent functions. In this work, the following expression for B is used:
B/MPa ) b0 + b1(T - T0 /K) + b2(T - T0 /K)2
(2)
and C is assumed to be temperature-independent. F(0.1 MPa, T) is the density at 0.1 MPa, interpolated by the following correlation:
F(0.1 MPa,T)/kg · m3 ) a0 + ai(T - T0 /K)
(3)
where T0 ) 273.15 K in all cases. The coefficients were obtained using the Marquardt’s algorithm and are given in Table 2 along with the standard deviation for each composition. Figure 3 presents the experimental densities and the fitted surfaces of alkanol (1) + linalool (2) versus x1 and P at (283.15 and 328.15) K. DeriWed Properties: Isobaric Thermal Expansion, rP, Isothermal Compressibility, KT, and Excess Molar Volume, VmE. Differentiating eq 1 with respect to temperature and pressure, the isobaric thermal expansion, RP, and the isothermal compressibility, κT, can be evaluated taking into account their definition:
1 ∂F RP ) F ∂T
( )
P
(4)
Figure 2. Comparison of densities for pure compounds vs pressure shown as the deviation (Fexp/Flit - 1) between experimental values of this work and literature values. (a) Differences for ethanol: 4, ref 17 at 313.15 K; s, ref 16 at 298.15 K; +, ref 20 at 313.15 K; O, ref 15 at (283.15 and 313.15) K; 0, ref 19 at (298.15 and 313.15) K; ×, ref 18 at 313.15 K. Differences between experimental values of this work and interpolated values from literature: (b) propan-1-ol: ×, ref 21 at (283.15, 298.15, 313.15, and 328.15) K; O, ref 23 at (313.15 and 328.15) K; +, ref 24 at (298.15, 313.15, and 328.15) K; (c) propan-2-ol: ×, ref 22 at (283.15, 298.15, 313.15, and 328.15) K; O, ref 23 at (313.15 and 328.15) K.
κT )
1 ∂F F ∂P
( )
T
(5)
It is well-known26 that analytical differentiation of the Tait equation with respect to pressure is certainly the most direct
Journal of Chemical & Engineering Data, Vol. 55, No. 11, 2010 5335 Table 2. Fitting Coefficients of Equation 4 for the Pure Liquids and Mixtures (Ethanol + Linalool), (Propan-1-ol + Linalool), and (Propan-2-ol + Linalool) and Standard Deviations sa Ethanol (1) + Linalool (2) a0/kg · m-3 a1/kg · m-3 · K-1 b0/MPa b1/MPa · K-1 b2/MPa · K-2 c0 s/kg · m-3 -3
a0/kg · m a1/kg · m-3 · K-1 b0/MPa b1/MPa · K-1 b2/MPa · K-2 c0 s/kg · m-3
x1 ) 0
x1 ) 0.1129
x1 ) 0.1935
x1 ) 0.3049
x1 ) 0.4023
x1 ) 0.5121
877.781 -0.8433 134.5 -1.3311 0.00931 0.08747 0.098
875.330 -0.8420 120.0 -1.1148 0.00735 0.08059 0.096
874.153 -0.8401 128.2 -1.252 0.00877 0.08553 0.12
871.349 -0.8420 125.1 -1.2515 0.00908 0.08478 0.12
868.534 -0.8473 114.8 -1.234 0.00941 0.07818 0.12
863.910 -0.8450 121.5 -1.270 0.00959 0.08447 0.12
x1 ) 0.6055
x1 ) 0.7008
x1 ) 0.8009
x1 ) 0.9009
x1 ) 1
858.870 -0.8432 121.1 -1.258 0.00958 0.08671 0.14
851.703 -0.8431 97.77 -1.048 0.00797 0.07317 0.15
841.328 -0.8401 107.2 -1.114 0.00855 0.08422 0.16
826.827 -0.8447 103.5 -1.007 0.00719 0.08840 0.14
806.523 -0.8698 88.7 -0.7919 0.00458 0.08584 0.12
Propan-1-ol (1) + Linalool (2) -3
a0/kg · m a1/kg · m-3 · K-1 b0/MPa b1/MPa · K-1 b2/MPa · K-2 c0 s/kg · m-3 a0/kg · m-3 a1/kg · m-3 · K-1 b0/MPa b1/MPa · K-1 b2/MPa · K-2 c0 s/kg · m-3
x1 ) 0
x1 ) 0.1070
x1 ) 0.2060
x1 ) 0.3066
x1 ) 0.4064
x1 ) 0.5010
878.103 -0.8415 128.7 -1.068 0.00624 0.08656 0.13
875.529 -0.8370 131.8 -1.182 0.00771 0.08839 0.10
873.435 -0.8366 124.5 -1.198 0.00841 0.08342 0.11
870.635 -0.8360 129.4 -1.161 0.00760 0.08888 0.11
867.551 -0.8385 119.0 -1.251 0.00890 0.08834 0.12
863.931 -0.8376 116.8 -1.171 0.00867 0.08114 0.14
x1 ) 0.6034
x1 ) 0.7055
x1 ) 0.7985
x1 ) 0.8980
x1 ) 1
858.841 -0.8343 111.3 -1.121 0.00829 0.07917 0.14
852.154 -0.8308 111.9 -1.186 0.00896 0.08032 0.14
844.285 -0.8202 113.4 -1.170 0.0089 0.08434 0.14
833.491 -0.8112 105.1 -1.008 0.00730 0.08336 0.13
819.137 -0.8102 92.7 -0.8204 0.00526 0.08005 0.090
Propan-2-ol (1) + Linalool (2) -3
a0/kg · m a1/kg · m-3 · K-1 b0/MPa b1/MPa · K-1 b2/MPa · K-2 c0 s/kg · m-3 a0/g · cm-3 a1/g · cm-3 · K-1 b0/MPa b1/MPa · K-1 b2/MPa · K-2 c0 s/kg · m-3
x1 ) 0
x1 ) 0.1031
x1 ) 0.2049
x1 ) 0.3054
x1 ) 0.4056
x1 ) 0.5022
878.103 -0.8415 128.7 -1.068 -0.00624 0.08658 0.13
874.875 -0.8401 120.2 -1.098 0.00750 0.08176 0.13
871.338 -0.8434 125.07 -1.210 0.00869 0.08566 0.14
867.374 -0.8513 116.4 -1.155 0.00808 0.08093 0.12
862.894 -0.8584 121.9 -1.253 0.00905 0.08587 0.15
857.761 -0.8669 121.0 -1.288 0.00962 0.08701 0.15
x1 ) 0.6055
x1 ) 0.7008
x1 ) 0.7981
x1 ) 0.9092
x1 ) 1
851.295 -0.8770 117.3 -1.399 0.0115 0.08510 0.19
843.643 -0.8822 113.7 -1.278 0.01010 0.08693 0.17
833.698 -0.8833 111.2 -1.347 0.0112 0.08751 0.23
818.359 -0.8766 99.22 -1.240 0.01045 0.08356 0.23
802.614 -0.8702 104.8 -1.168 0.01035 0.09464 0.24
a
s)
N
∑ (F
i,exp
- Fi,calc)2/(N - P)
i)1
where N ) number of experimental points and P ) number of adjustable parameters.
way to obtain reliable isothermal compressibility data. The calculated isothermal compressibility was estimated to have an expanded uncertainty (k ) 2) of ( 14 TPa-1. In a similar way, isobaric thermal expansion data can be determined from analytical calculation following Cerdeirin˜a et al.27 and Troncoso et al.28 RP was evaluated in the investigated pressure and temperature ranges finding an expanded uncertainty (k ) 2) of ( 0.005 kK-1. Uncertainties
for isothermal compressibility and isobaric expansion were obtained following the statistical method of propagation of uncertainty. The calculated values of κT and RP are given respectively in Tables S1 and S2 of Supporting Information. Figure 3 shows the calculated values of these properties for the alkanol (1) + linalool (2) mixtures versus x1 and P at (283.15 and 328.15) K.
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Journal of Chemical & Engineering Data, Vol. 55, No. 11, 2010
Figure 3. Experimental density, F, excess molar volume, VmE, and fitted surfaces, calculated isobaric thermal expansion, RP, and calculated isothermal compressibility, κΤ, for the mixtures: (a) ethanol (1) + linalool (2); (b) propan-1-ol + linalool (2); and (c) propan-2-ol (1) + linalool (2) vs mole fraction and pressure at b, 283.15 K and O, 328.15 K. Contour plots appear at the bottom of the figures.
For the three binary systems within the considered T, P range and composition, the isothermal compressibility, as well as the isobaric thermal expansion, increases, as usually, with increasing temperature and decreases with increasing pressure. The pure compounds in the conditions of this work exhibit the following sequences:
RP(ethanol) ≈ RP(propan-2-ol) > RP(propan-1-ol) ≈ RP(linalool)
κT(ethanol) ≈ κT(propan-2-ol) > κT(propan-1-ol) > κT(linalool) These series could help us to explain the behavior of both derived properties among a binary mixture. As it can be observed for the three systems, the isothermal compressibility shows a monotonically increasing behavior as a function of the alcohol concentration, x1. Similar results are found for the isobaric thermal expansion coefficient in relation with the ethanol + linalool and propan-2-ol + linalool systems. In
Journal of Chemical & Engineering Data, Vol. 55, No. 11, 2010 5337 Table 3. Fitting Coefficients of Equation 7 for the Mixtures (Ethanol + Linalool), (Propan-1-ol + Linalool), and (Propan-2-ol + Linalool) and Standard Deviations s at the Given (p, T) Conditionsa P/MPa 0.1
5
P/MPa
10
15
20
0.1
5
10
15
20
Ethanol (1) + Linalool (2) A1 · 106/m3 · mol-1 A2 · 106/m3 · mol-1 A3 · 106/m3 · mol-1 s · 106/m3 · mol-1
-2.400 -0.767 0.969 0.02
-2.299 -0.718 0.907 0.02
T/K ) 283.15 -2.244 -0.680 0.959 0.02
-2.183 -0.621 0.965 0.02
-2.096 -0.562 0.831 0.02
-2.566 -0.925 0.722 0.03
-2.470 -0.863 0.730 0.02
T/K ) 298.15 -2.391 -0.827 0.820 0.02
-2.293 -0.787 0.721 0.02
-2.247 -0.714 0.767 0.02
A1 · 106/m3 · mol-1 A2 · 106/m3 · mol-1 A3 · 106/m3 · mol-1 s · 106/m3 · mol-1
-2.683 -1.02 0.644 0.03
-2.596 -1.02 0.6663 0.03
T/K ) 313.15 -2.514 -0.892 0.673 0.03
-2.419 -0.881 0.648 0.03
-2.349 -0.836 0.664 0.03
-2.795 -1.14 0.344 0.03
-2.662 -1.07 0.380 0.03
T/K ) 328.15 -2.535 -0.966 0.344 0.02
-2.457 -0.936 0.411 0.02
-2.364 -0.902 0.404 0.02
-1.672 -0.765 0.918 0.01
-1.642 -0.706 1.016 0.01
-1.898 -0.903 0.593 0.01
-1.852 -0.871 0.579 0.009
T/K ) 298.15 -1.791 -0.788 0.657 0.01
-1.745 -0.767 0.606 0.01
-1.704 -0.695 0.610 0.01
-1.800 -0.686 0.752 0.009
-1.717 -0.705 0.491 0.009
-1.878 -0.807 0.139 0.01
-1.822 -0.800 0.342 0.01
T/K ) 328.15 -1.753 -0.765 0.329 0.01
-1.718 -0.734 0.308 0.01
-1.676 -0.698 0.307 0.01
Propan-1-ol (1) + Linalool (2) A1 · 106/m3 · mol-1 A2 · 106/m3 · mol-1 A3 · 106/m3 · mol-1 s · 106/m3 · mol-1
-1.862 -0.822 0.717 0.009
-1.814 -0.707 0.809 0.009
T/K ) 283.15 -1.713 -0.805 1.046 0.009
A1 · 106/m3 · mol-1 A2 · 106/m3 · mol-1 A3 · 106/m3 · mol-1 s · 106/m3 · mol-1
-1.916 -0.847 0.336 0.01
-1.864 -0.820 0.347 0.01
T/K ) 313.15 -1.829 -0.765 0.477 0.01
-1.223 -0.899 0.02
-1.151 -0.767 0.02
-1.273 -0.827 0.01
-1.236 -0.789 0.02
T/K ) 298.15 -1.205 -0.741 0.01
-1.173 -0.672 0.02
-1.137 -0.683 0.02
-1.070 -0.420 -0.213 0.01
-1.041 -0.444 0.01
-1.049 -0.343 -0.301 0.01
-1.025 -0.324 0.01
T/K ) 328.15 -0.953 -0.338 -0.200 0.01
-0.948 -0.263 0.01
-0.920 -0.276 0.01
Propan-2-ol (1) + Linalool (2) A1 · 106/m3 · mol-1 A2 · 106/m3 · mol-1 A3 · 106/m3 · mol-1 s · 106/m3 · mol-1
-1.349 -0.891 0.02
-1.340 -0.879 0.02
T/K ) 283.15 -1.238 -0.930 0.02
A1 · 106/m3 · mol-1 A2 · 106/m3 · mol-1 A3 · 106/m3 · mol-1 s · 106/m3 · mol-1
-1.165 -0.545 -0.264 0.02
-1.113 -0.549 -0.289 0.02
T/K ) 313.15 -1.068 -0.484 -0.236 0.02
a
s)
N
∑ (V
E mi,exp
E - Vmi,calc )2/(N - P)
i)1
where N ) number of experimental points and P ) number of adjustable parameters.
the other side, the minimal changes of RP with x1 observed for the propan-1-ol + linalool system are a logical consequence of the similar values of RP for the pure compounds. In general, taking the x-axis as a reference, the convex shape established for κT and RP versus x1 could be explained as the result of a decrease in the free volume of the molecules within the mixtures. Excess molar volumes as a function of the alcohol molar fraction, x1, were determined at each P, T from densities of the two pure liquids, F1 and F2, and from that of their mixtures, F, according to the relation:
(
E Vm (P, T) ) x1M1
)
(
1 1 1 1 + x2M2 F F1 F F2
)
(6)
where M1 and M2 are the molar masses of alkanol and linalool, respectively. Table S3 of Supporting Information reports the calculated values of excess molar volumes. The estimated uncertainty on VmE is ( 5 · 10-8 m3 · mol-1. This excess quantity was fitted to the Redlich-Kister equation: E Vm (P, T)/m3 · mol-1 ) x1x2(A1 + A2(2x1 - 1) +
A3(2x1 - 1)2)
(7)
where x1 and x2 are the molar fractions of alkanol and linalool, respectively, and Ai are the fitting parameters. The values of the Ai parameters and the standard deviations are shown in Table 3. The variation of the excess molar volume and the fitted surface versus the composition of alkanol and pressure is also shown at (283.15 and 328.15) K in Figure 3. For all of the mixtures in the whole T, P range, this magnitude is negative (minimum x1 ≈ 0.60). Such relatively high negative values of excess volumes surely are the consequence of strong, oriented interactions such as hydrogen bonds due to alcohol groups. As a result these mixtures are better packed than the pure compounds. As Figure 3 shows, |VmE| increases with the associating capacity of the alkanol, and the diagrams also Table 4. Pure Component Properties Used for the Application of the Equations of State compound a
ethanol propan-1-ola propan-2-ola linalool
Mw
Tc
Pc
Tb
g · mol-1
K
MPa
K
46.096 60.096 60.096 154.249
513.90 537.32 508.30 634.65c
6.148 5.182 4.7616 2.582c
351.4 370.3 355.4 471.2d
ω 0.644b 0.618b 0.665b 0.761b
Ref 32. b Calculated using Lee-Kesler method, ref 30. c Calculated using Joback’s method, ref 29. d Ref 1. a
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Journal of Chemical & Engineering Data, Vol. 55, No. 11, 2010
Table 5. Pure Component Parameters Used for the Application of the Studied Equations of State m
υoo/L · mol-1
uo/k/K
κ
/k/K
2.457 3.240 3.249 5.453
0.0120 0.0120 0.0120 0.0176
213.48 225.68 202.94 247.83
0.02920 0.01968 0.02095 0.02310
2759 2619 2670 2026
SAFT 4
ethanol propan-1-ol4 propan-2-ol4 linalool PC-SAFT
mi
σi/Å
i/k/K
κAiBi
AiBi/k/K
ethanol8 propan-1-ol8 propan-2-ol8 linalool
2.3827 2.9997 3.0929 4.1979
3.1771 3.2522 3.2085 3.9193
198.24 233.40 208.42 271.74
0.032384 0.015268 0.024675 0.001912
2653.3 2276.8 2253.9 2187.3
Table 6. Absolute Average Percentage Deviation, AADa, for the Correlation of Saturation Properties and Prediction of Compressed Liquid Density compound
EOS
linalool
PR SAFT PC-SAFT
AAD Psat AAD Fsat ∆Tc/K ∆Pc/MPa AAD Fcomp
25.84 5.69 4.70
5.75 1.80 0.25
57.65 44.05
0.248 0.391
3.80 2.23 0.26
a AAD ) 100/N · ∑|Fi,EOS - Fi,exp|/Fi,exp where N ) number of points; ∆Tc ) Tc,EOS - Tc and ∆Pc ) Pc,EOS - Pc.
illustrate differences with the temperature for the three binary systems. The excess volume of the system (linalool + propan1-ol) appears as practically temperature-independent, and the systems containing ethanol and propan-2-ol show an opposite behavior. Apart from molecular packing considerations, this thermal inversion could be well explained on the basis of an opposite change with temperature of the overall interactions for the mixtures (ethanol + linalool), (propan-1-ol + linalool), and (propan-2-ol + linalool). Equations of State (EOS’s). Three EOS’s were tested in this work to predict the PFT behavior of the fluid mixtures. One of them is a cubic equation put forward by PR,3 and the other two are based on the theory of perturbations: the SAFT (Huang and Radosz’s version)4-6 and PC-SAFT.7,8 The needed properties of the pure components are gathered in Table 4. Critical properties of linalool were calculated according to Joback’s method,29 and the acentric factor was estimated using the Lee-Kesler method.30 The EOS parameters for linalool were evaluated from the correlation of vaporpressure properties,31 and liquid densities were extrapolated by eq 1. Table 5 shows the parameters obtained for linalool together with those of the alkanols found in the literature. The absolute average percentage deviation values (AAD) of saturation properties of pure linalool are shown in Table 6. To determine the PFT behavior of linalool + alkanol mixtures, the van der Waals one-fluid mixing rules were used, and classical quadratic combining rules for the cross-terms were selected in all cases. PR, SAFT, and PC-SAFT were tested as predictive models, so all of the binary interaction parameters were considered equal to zero. The obtained results with the three equations of state are listed in Tables S4, S5, and S6 of Supporting Information. The best results for the predictions of experimental compressed densities of the binary mixtures under study were achieved with PCSAFT, Figure 4. The ADD obtained for PC-SAFT for (ethanol + linalool), (propan-1-ol + linalool), and (propan-2-ol + linalool) were (0.44, 0.76, and 0.45) %, respectively. For the same three binary systems, the results achieved for PR and SAFT were (2.88, 1.82, and 2.19) % and (2.88, 2.50, and 2.11) %. Despite the similar ADD for PR and for SAFT equation, SAFT describes more adequately the behavior of the density with the mole composition of the mixture.
Figure 4. Residuals of density predictions of three EOS’s, kij ) 0, for the mixtures (a) ethanol (1) + linalool (2); (b) propan-1-ol (1) + linalool (2); and (c) propan-2-ol (1) + linalool (2) at 283.15 K and 20 MPa (filled symbols) and at 328.15 K and 0.1 MPa (open symbols): 0, PR; O, SAFT; 4, PC-SAFT.
Conclusion The density of nine compositions of three binary systems, (ethanol + linalool), (propan-1-ol + linalool), and (propan-2-
Journal of Chemical & Engineering Data, Vol. 55, No. 11, 2010 5339
ol + linalool), has been measured in the range (283.15 to 328.15) K and up to 20 MPa with an overall uncertainty of ( 0.5 · kg · m-3. Isothermal compressibilities, isobaric thermal expansivities, and excess molar volumes, as well as their dependencies on temperature, pressure, and composition, have been obtained. A negative behavior of the excess molar volume versus composition has been found; moreover, depending on the binary system, this magnitude exhibits an opposite trend with temperature probably due to the different hydrogen-bond capacity of the different alkanols. PR, SAFT, and PC-SAFT have been tested to predict the PFT equilibrium of the binary systems under study. The best results of the compressed densities of the mixtures are obtained using PC-SAFT with an overall ADD of 0.55 %. PC-SAFT appears as an invaluable tool to predict the PFT behavior of the mixtures linalool + alkanols from only the vapor-liquid equilibrium and the saturated density of the pure components. Supporting Information Available: Calculated values of the isothermal compressibilities, the isobaric thermal expansions, and the excess molar volumes for the alkanol + linalool mixtures. PFT predictions of PR, SAFT, and PC-SAFT equations of state. This material is available free of charge via the Internet at http://pubs.acs.org.
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